NAG has recently started an academic collaboration with the Centre for Doctoral Training in Industrially Focused Mathematical Modelling (InFoMM) at the University of Oxford. Lindon Roberts is the main researcher supervised by Coralia Cartis, Associate Professor in Numerical Optimization. NAG is a strong supporter of InFoMM, offering student projects, providing training courses and sitting on the Industrial Engagement Committee.
This project focuses on mathematical optimization where derivatives are not readily available, so called derivative-free optimization (DFO). It is not easy or even possible to evaluate derivatives of functions which appear in the optimization model and thus many well-established approaches in mathematical optimization might not be satisfactory. Moving to a derivative-free regime presents novel approaches for approximating the solution without computing or estimating derivatives. NAG added its first derivative-free solver to the NAG Library about five years ago. Since then this field has attracted significant academic attention, resulting in numerous advances.
NAG started the collaboration with Lindon, Coralia and the InFoMM CDT earlier this year when a mini-project was sponsored to investigate DFO for nonlinear least squares optimization, a problem which is very common in the calibration of models in finance and engineering. After successful completion, NAG received not only a review of state-of-the-art DFO software, but also a working solver which will be adopted into the Library in 2017. We believe it will be the first such commercial solver available to the public anywhere in the world.
The full Doctoral project will focus on several open problems in DFO such as performance for noisy problems and the curse of dimensionality for large-scale problems. NAG will assist throughout the project by providing technical expertise and guidance, and by collaborating closely with Lindon to integrate his research into the NAG Library, enabling smooth and timely commercialisation of his research.
Academic collaborations remain a core part of our business and help the adoption of cutting-edge research into the NAG Library. The optimization software in the Library is an important part of its value to our customers and Lindon’s research into new techniques for DFO will enhance this further. We look forward to the continuation of this research.